April 02, 2012

Craster's daughters

The second season of Game of Throneshas started and the series has become the topic of somefun discussion, I thought I'd give my €0.02 on the topic of genetic improbabilities.

(A warning: I have only read the first book, so please refrain from spoiling in the comments. Also, this post contains a minor spoiler about the first episode of season 2)

One of the good things about fiction is that it brings up interesting probabilities that would not often come up in the real world. In the first episode of Season 2, we are introduced to Craster, a character who lives north of the Wall. The interesting thing about Craster is that he practices a combination of incest and infanticide: he exposes his male offspring and weds his daughters, repeating the cycle. Let's examine whether or not this scenario is plausible:

In the first generation, Craster would have a 50% coefficient of relatedness with his daughters.

In the second generation, this would increase to 75%. In the third, this would be 87.5%, etc.

What is interesting is that their autozygosity would also increase across the generations.

In the first generation, at a random locus the probability that both copies have been inherited from the same ancestor is some random number corresponding to the probability of identity-by-descent in the general population.

In the second generation, at half the loci there is a 50-50 chance that the same allele will be inherited from Craster, hence the grand-daughters will be autozygous across at least 25% of the genome. This means that they will be homozygous for about a quarter of Craster's deleterious genetic load.

When we first see Craster, he seems to have quite a few "wives", so my guess is that this has been going on for 2-3 generations at least, which seems plausible given the early age of marriage in a quasi-medieval world.

However, given the severe abnormalities observed in children of father-daughter incest it will become increasingly difficult for Craster to obtain viable offspring through this practice. Many of his children would be aborted, die, or be severely incapacitated.

In order to increase his harem's size (as he seems to be doing) he would need each of his wives to produce 2 daughters for him. This translates to an average of 4 offspring per daughter (since 2 boys will also be born, on average, and exposed).

But, due to high levels of autozygosity, many of Craster's offspring would not be viable; hence, each wife must undergo a very large number of pregnancies. And, given that each wife is heavily inbred herself, she is less likely to survive many pregnancies, especially since there's no ob/gyn north of the Wall.

In conclusion, the tale of "Craster and his Wives" does seem to fit well in a work of fantasy...

17 comments:

In house Targaryan, brother and sister have children, to "keep the bloodline clean" (and to keep the possibly genetical inheritated ability to be immune against fire...hehehe). And thats since 300 years.

Hm. Well, on the other hand, if the immunity against fire would be a genetical trait, Danys brother would, beeing the result of 300 years of incest, be a clone of his sister and so, should be immune to fire and was not.

What just springs to my mind:10 or so years ago, geneticans claimed the possibility of people beeing better suited against incest, because they had been genetical "more diverse". They claimed, modern humans are all the result of extreme incest, saying stuff like: "2 humans from 2 different continents are genetical more similiar than 2 chimpansee who belong to the same tribe..."

And if we think, Cruster and his first wife had been more different than modern humans, he can incest for more generations in a row than a modern human, without problems?

The Targaryen strategy is equivalent to having a population with an effective size of 2. They are subject to extreme genetic drift, and over a number of generations, all the offspring will be completely homozygous, with the unique allele at each locus being drawn from either of the original pair.

The Craster strategy is even worse: the effective population size is less than 2. Moreover, it cannot be pursued indefinitely, since it depends on Craster living and being able to do his husbandly duties, which must come to an end at some point.

_If_ Craster was really able to pursue it, his final batch of daughters would be nearly all homozygous, where all the alleles being ultimately drawn from himself.

So, Craster's strategy is even less believable than the Targaryen one, and is rendered less believable by the fact that the Craster pool of daughters seems to be growing exponentially _despite_ the fact that his progeny are worse off genetically _and_ must deal with much harder living/breeding conditions.

Simply because its just for a few generations. And I think that the problems coming with incest are extremely exaggerated.

To my understanding, its all about damaged/wrong copied genes?

Wich, if 2 genetical totaly different people mate, have a good chance to be "repaired" (by inheritating an undamaged version) while in in an incest case, the damaged genes are copied all over and over again and never beeing "repaired"?

Also, there are "Crusters" in real life. Possibly just in this minute. Keeping their doughters in the cellar and breeding with them and then with their doughters doughters....

> In conclusion, the tale of "Craster and his Wives" does seem to fit well in a work of fantasy...

It's technically possible to have normal kids if each time the daughters only passed the genetic material from her mother. Without crossover that would be like, what, 1/(2^23) each time that happens. Totally feasible man! : )

" Keeping their doughters in the cellar"

Lol, those daughters weren't in a cellar and they murdered their sons.

I disagree. Incest is socially unacceptable, but biologically not as bad as many people think. Breeders (not of humans) routinely do this. It raises the chances of unviable offspring, but there are always a large number of perfectly healthy offspring, and genes that cause weird issues recessively are rapidly removed. Do you have any science to support your case?

"Twenty-nine children of brother-sister or father-daughter matings were studied. Twenty-one were ascertained because of the history of incest, eight because of signs or symptoms in the child. In the first group of 21 children, 12 had abnormalities, which were severe in nine (43%). In one of these the disorder was autosomal recessive. All eight of the group referred with signs or symptoms had abnormalities, three from recessive disorders. The high empiric risk for severe problems in the children of such close consanguineous matings should be borne in mind, as most of these infants are relinquished for adoption."

http://www.sciencedirect.com/science/article/pii/S0022347682803478

Do you have any science to support your case?

Do you have any data to support your case that it is "biologically not as bad as many people think?"

Dienekes, apart from the movies, this sort of a breeding plan has been implemented in reality by some Mormon fundamentalists (such as Allreds, Lamb of God) to purify the seed of Jesus and thus hasten the Millennium. I don't think they went over more than a single iteration though.

"And I think that the problems coming with incest are extremely exaggerated. To my understanding, its all about damaged/wrong copied genes?"

It is about 'damaged/wrong copied genes' but everybody has them. They are usually obscured by dominant alleles. The problems with incest may be exaggerated for a single generation but over several they become severe.

"Breeders (not of humans) routinely do this. It raises the chances of unviable offspring, but there are always a large number of perfectly healthy offspring"

I don't know about 'a large number of perfectly healthy offspring'. I think poultry breeders are the only people I know of that do it, and then only to breed the 'perfect' show fowl. And they have to destroy a significant number of deformed chickens in a hatch of several hundred.

"In order to increase his harem's size (as he seems to be doing) he would need each of his wives to produce 2 daughters for him. This translates to an average of 4 offspring per daughter (since 2 boys will also be born, on average, and exposed)".

The problem is that the first problem that appears during inbreeding is usually a huge drop in fertility, either through inability to conceive or a high abortion rate.

"Twenty-nine children of brother-sister or father-daughter matings were studied. Twenty-one were ascertained because of the history of incest, eight because of signs or symptoms in the child"

The research you quoted D, is a bit dodgy. If 8 were ascertained through symptoms, the research can't tell us anything about the percentage of babies born with negative symptoms as a result of incestuous unions.

Obviously though, it is higher than that in in non-incestuous unions, as it is an extreme case of the type of situation that causes problems for isolated endogamous populations.

Though I think genetics are different on Westeros, as you move through the books you'll see focus on eye and hair colour inheritance that seems to be different from our world.

"Did not the Egyptian pharaohs routinely marry brother and sister? How long did that go on, and how did it turn out?"

I recall that this was teached in Histoy class at my time too. (1980s)

Back then, it was said, the Pharao lineage had weak health and a frequently a bunch of unusual mental illnesses and aborations because of the Targaryen style incest (they said, the Pharao is of the blood of the gods and so, cant merry with a "mortal". to keep the divine blood clean, he must have offspring with his sister)

Fifth attempt. This time I'm going to sign up for a completely unwanted blogger account rather than killing it when it tries to make me sign up for a blog and see if it gets through.

First, a nit. In the sentence beginning "In the second generation," I think you meant "daughter" instead of "Craster."

In a more serious vein, I think the analysis would be better if you assumed that each generation has Craster's original DNA as an input. If you do, then two things happen. First, the other parent's DNA becomes less and less significant, and second, the horde of daughters stabilizes. Because each generation has original Craster DNA, the sites where he's homozygous will tend to become homozygous, and the ones where he's heterozygous will tend to have all three possible variants in the offspring - including homozygous in both variants. In other words, some of the sites where Craster has deleterious recessives will have double doses of healthy variants in some of the daughters.

"Because each generation has original Craster DNA, the sites where he's homozygous will tend to become homozygous, and the ones where he's heterozygous will tend to have all three possible variants in the offspring - including homozygous in both variants"

And it is those homozygous genes that give rise to problems. In Craster himself deleterious recessive genes will be obscured by non-disadvantageous dominant genes. But many of his obscured recessives will be disadvantageous in some way.

"In other words, some of the sites where Craster has deleterious recessives will have double doses of healthy variants in some of the daughters".

Soe of the daughters will have 'double doses of healthy variants' but when they in turn have daughters to Craster half the daughters will carry the deleterious genes, and pass them on to half their own offspring. Considering just one of those deleterious genes we could maintain that the decline would be slow. But remember Craster almost certainly has more than just one deleterious recessive gene, greatly increasing the rate of decline.

"Do you have any data to support your case that it is 'biologically not as bad as many people think?'"

I think the data you posted supports my point strongly. Out of 21 children of incest, 9 did not have any abnormalities. Do you think Craster would care if 15 daughters died or were killed for every 9 wives he gained? Craster didn't have any old wives (in either the book or the movie), but obviously had wives many years ago, what do you think happened to them?

We can hypothesize these 9 children had problematic genes bred out and would be less likely to have abnormal children if bred with their parents. Or we can hypothesize they will have a higher rate of abnormalities because they share even more DNA with their parents. Either way, more than enough children are produced for a "Craster" to exist.

We are not talking about a sustained "Craster" population for thousands of years, we are talking about 4 generations at most.

I think the data you posted supports my point strongly. Out of 21 children of incest, 9 did not have any abnormalities

Do you realize what you are saying? Each wife would need to undergo a total of ~5 pregnancies in order to produce a normal daughter.

If you think that's "not so bad as people think", then no comment.

We can hypothesize these 9 children had problematic genes bred out and would be less likely to have abnormal children if bred with their parents.

Incorrect. Each daughter generation gets a fresh input of 50% of Craster's deleterious genetic load. The population does _not_ become asymptotically healthier: abnormal children are continually produced with Craster's strategy.

Also, would Cruster have many unhealthy variants, if the world would be Creationist-Style, like many Fantasy worlds are suposed to be? (I recall the age of the planet Krynn (d&d Dragonlance) is suposed to be just 10K years)

Well, ok in Game of Thrones, all ages are extreme. Bronce Age 10K years ago (Quiet slow development). Wall was build 7K years ago. Castle "Winterfell" has a similiar age. Most noble houses rule since 5K-10K years (!!!)

Still, there is this possibility of that world beeing created in "creationist-style"... POOF... by a one or more gods (possibly these 2 from that Dualism of the red priests. The Fire god and the Ice god, since the whole book series is named after these? ("Song of Ice and Fire")

Wouldnt the genes of a species that only exists since a few K years be much "healthier" than the ones of a species whos DNA accumulates errors since 350 Million years?

"Do you realize what you are saying? Each wife would need to undergo a total of ~5 pregnancies in order to produce a normal daughter".

Exactly. And that is why such mating is possible in poultry where hundreds of eggs can be hatched at the same time. Mind you, you have to be able to get those hundreds of eggs from the parent population and usually hens from such matings produce far fewer eggs than do hens with any level of hybrid vigour. That holds true even for purebreds. Most close matings in poultry are made for 'type' rather than egg production, so wastage is not too important.

Again, exactly. So even with just one original deleterious recessive gene carried by both Craster and the relevant daughter one quarter of the offspring are 'unfit'. A further half will carry the recessive gene to pass it on to their descendants.

"would Cruster have many unhealthy variants, if the world would be Creationist-Style, like many Fantasy worlds are suposed to be?"

True, but I think we're talking here of what is more likely to be the case in real life.

"Wouldnt the genes of a species that only exists since a few K years be much 'healthier' than the ones of a species whos DNA accumulates errors since 350 Million years?"

Not necessarily so because genes are mutating all the time to form advantageous, deleterious and neutral variants. It would depend on the mutation history of the species.

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